Physical Laws Research Articles

Self-Replication Without Hydrogen-Bonds: An Exobiotic Design.

Life on Earth uses DNA as the central template for self-replication, genetic encoding, and information transfer. However, there are no physical laws precluding life's existence elsewhere in space, and alternative life forms may not need DNA. In the search for exobiology, knowing what to look for as a biosignature remains a challenge - especially if it is not from the obvious list of biologic building blocks. Clues from chemicals recently discovered on Mars and in the Taurus Molecular Cloud 1 (TMC-1), show that intriguing organic compounds exist beyond Earth, which could provide a starting point for unconventional exobiotic designs. Here we present a new potential self-replicating system with structural similarities to recently discovered compounds on Mars and TMC-1. Rather than using DNA's hydrogen-bonding motif for reliable base-paring, our design employs sulfur-nitrogen interactions to selectively template unique benzothiadiazole units in sequence. We synthesized and studied two versions of this system, one reversible and the other irreversible, and found experimental evidence of self-replication in d-chloroform solvent. These results are part of a larger pursuit in our lab for developing a basis for a potential exobiological system using starting blocks closely related to these cosmic compounds.

A thousand converging paths to self-observation and self-discovery: science, spirituality and philosophical practice

This article aims to connect dots from different schools of thought and argues for the importance of an interdisciplinary approach to any subject matter and the immense potential the virtually endless openings thus created can represent for philosophical counseling. It brings arguments on the importance of understanding from linguistic nuances, in any strict systematic discipline that builds and organizes knowledge in the form of testable hypotheses and predictions about the world, to various symbolic systems of spiritual practices. It emphasizes the formal logic of mathematics – which comes from the ancient Greek notion máthēma (μάθημα), meaning "that which is learned", "what one gets to know", hence also "study" and "science" – in an attempt to simplify complexities but also the importance, for one’s philosophical journey to self-harmonization with existence, of a large number of alternative types and forms of reconstruction of reality devised by mankind. By employing pure or applied mathematics thinking patterns – if addressed to scientifically-minded interlocutors –, philosophy qua practice can build bridges between disciplines by cross-translating specific glossaries, focusing on referential points, and emancipative essences, and smoothing sharp edges - in the search for a broader, common denominator, and collective viewpoint. For instance, for clients with advanced scientific backgrounds and high expectations, it can start the dialogic reflections from philosophy’s own sophisticated toolset able explain the Doppler shift of psychohistory, by de-noising - in midair - the different observable perspectives, in the multipolar, prone to gridlock, umwelt of humanity. For other clients, less scientific yet read and inclined towards objective realism, philosophical counseling can still start their transformative journey from anchoring their worldviews in the fact that the laws of physics are here to stay, yet suggesting the adoption of the observer effect through which, in our commuting with nature, neutrality can have a harmonizing effect on the viability of what constitutes the "is", starting from the individual "know thyself", continuing with the containing physical, ideological, spiritual frameworks to identify inflection points and prepare next adjacencies for evolution in the collective reality. For many other potential philosophically inclined clients, other spiritual practices such as various religions or meditation are crucial coordinates of their lives and around which philosophical counselors can revolve the dialogue. Yet other people are inclined to philosophize through favorite insightful song lyrics and melodies. Philosophical counseling can help to leave no one behind in terms of finding meaning, decision grounding, and, or at least, peace. Whatever that might mean, on micro and macro levels. Building a philosophical journey "ark" needs a blueprint, and requires a list of "animals", a pair of each kind - the "good" and "bad" sides, hand in hand, of any identifiable entity - before it sets sail towards the unknown, the open sea. In the narrow neck of the present, in the sand clock between past and future every client who seeks assistance feels at the crossroads of the reflected side of "where do I/We come from" and the "where am/are I/We going! " regardless if "we" - as a collective - understand or not "what are We".

Large language models for automatic equation discovery of nonlinear dynamics

Equation discovery aims to directly extract physical laws from data and has emerged as a pivotal research domain in nonlinear systems. Previous methods based on symbolic mathematics have achieved substantial advancements, but often require handcrafted representation rules and complex optimization algorithms. In this paper, we introduce a novel framework that utilizes natural language-based prompts to guide large language models (LLMs) in automatically extracting governing equations from data. Specifically, we first utilize the generation capability of LLMs to generate diverse candidate equations in string form and then evaluate the generated equations based on observations. The best equations are preserved and further refined iteratively using the reasoning capacity of LLMs. We propose two alternately iterated strategies to collaboratively optimize the generated equations. The first strategy uses LLMs as a black-box optimizer to achieve equation self-improvement based on historical samples and their performance. The second strategy instructs LLMs to perform evolutionary operations for a global search. Experiments are conducted on various nonlinear systems described by partial differential equations, including the Burgers equation, the Chafee–Infante equation, and the Navier–Stokes equation. The results demonstrate that our framework can discover correct equations that reveal the underlying physical laws. Further comparisons with state-of-the-art models on extensive ordinary differential equations showcase that the equations discovered by our framework possess physical meaning and better generalization capability on unseen data.

Causal Modeling and Thermodynamics: Towards a new convergence of the two fields

In 1824, Nicolas Léonard Sadi Carnot paid for the publication of his first book. Unfortunately it sparked little interest, and the young engineer never published another. In quick succession, Carnot served in the military, suffered from scarlet fever, mania, and cholera, and passed away in obscurity at age 36. Two centuries have elapsed since Carnot published his only book. Recognition came later. In particular, Carnot's reasoning inspired scientists to formulate the first and second laws of Thermodynamics. The new science that has emerged around these physical laws is nothing short of breathtaking. Yet, with success and growth, critical attention and skepticism have followed. In 1924, Louis de Broglie lauded the first law of Thermodynamics, while remaining more reserved to wards the second. The first law builds on a long history rooted in Causal Modeling, while the second does less so. Today, physicists such as Adrian Bejan continue praising Thermodynamics but contend that some formulations of the second law may have attracted broken science. The present article revisits this history in an attempt to cut through some of the fog. As an outcome of this re-evaluation, the article outlines a new convergence of Thermodynamics and Causal Modeling.

Training coupled phase oscillators as a neuromorphic platform using equilibrium propagation

Abstract Given the rapidly growing scale and resource requirements of machine learning applications, the idea of building more efficient learning machines much closer to the laws of physics is an attractive proposition. One central question for identifying promising candidates for such neuromorphic platforms is whether not only inference but also training can exploit the physical dynamics. In this work, we show that it is possible to successfully train a system of coupled phase oscillators—one of the most widely investigated nonlinear dynamical systems with a multitude of physical implementations, comprising laser arrays, coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this end, we apply the approach of equilibrium propagation, which permits to extract training gradients via a physical realization of backpropagation, based only on local interactions. The complex energy landscape of the XY/Kuramoto model leads to multistability, and we show how to address this challenge. Our study identifies coupled phase oscillators as a new general-purpose neuromorphic platform and opens the door towards future experimental implementations.

Hidden turbulence in van Gogh's The Starry Night

Turbulent skies have often inspired artists, particularly in the iconic swirls of Vincent van Gogh's The Starry Night. For an extended period, debate has raged over whether the flow pattern in this masterpiece adheres to Kolmogorov's theory of turbulence. In contrast to previous studies that examined only part of this painting, all and only the whirls/eddies in the painting are taken into account in this work, following the Richardson–Kolmogorov's cascade picture of turbulence. Consequently, the luminance's Fourier power spectrum spontaneously exhibits a characteristic −5/3 Kolmogorov-like power-law. This result suggests that van Gogh had a very careful observation of real flows, so that not only the sizes of whirls/eddies in The Starry Night but also their relative distances and intensity follow the physical law that governs turbulent flows. Moreover, a “–1”-like power-law persists in the spectrum below the scales of the smallest whirls, hinting at Batchelor-type scalar turbulence with a high Schmidt number. Our study, thus, unveils the hidden turbulence captured within The Starry Night.

Demonstration of microwave single-shot quantum key distribution

Security of modern classical data encryption often relies on computationally hard problems, which can be trivialized with the advent of quantum computers. A potential remedy for this is quantum communication which takes advantage of the laws of quantum physics to provide secure exchange of information. Here, quantum key distribution (QKD) represents a powerful tool, allowing for unconditionally secure quantum communication between remote parties. At the same time, microwave quantum communication is set to play an important role in future quantum networks because of its natural frequency compatibility with superconducting quantum processors and modern near-distance communication standards. To this end, we present an experimental realization of a continuous-variable QKD protocol based on propagating displaced squeezed microwave states. We use superconducting parametric devices for generation and single-shot quadrature detection of these states. We demonstrate unconditional security in our experimental microwave QKD setting. The security performance is shown to be improved by adding finite trusted noise on the preparation side. Our results indicate feasibility of secure microwave quantum communication with the currently available technology in both open-air (up to ~ 80 m) and cryogenic (over 1000 m) conditions.

Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint

Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for spatio-temporal sparse field prediction fail to meet the accuracy and inference time required for nonlinear dynamic prediction problems. In this paper, we introduce the Dynamical System Prediction from Sparse Observations using Voronoi Tessellation (DSOVT) framework, an innovative methodology based on Voronoi tessellation which combines convolutional encoder–decoder (CED) and long short-term memory (LSTM) and utilizing Convolutional Long Short-Term Memory (ConvLSTM). By integrating Voronoi tessellations with spatio-temporal deep learning models, DSOVT is adept at predicting dynamical systems with unstructured, sparse, and time-varying observations. CED-LSTM maps Voronoi tessellations into a low-dimensional representation for time series prediction, while ConvLSTM directly uses these tessellations in an end-to-end predictive model. Furthermore, we incorporate physics constraints during the training process for dynamical systems with explicit formulas. Compared to purely data-driven models, our physics-based approach enables the model to learn physical laws within explicitly formulated dynamics, thereby enhancing the robustness and accuracy of rolling forecasts. Numerical experiments on real sea surface data and shallow water systems clearly demonstrate our framework’s accuracy and computational efficiency with sparse and time-varying observations.

Diffusion Correction in Fricke Hydrogel Dosimeters: A Deep Learning Approach with 2D and 3D Physics-Informed Neural Network Models.

In this work an innovative approach was developed to address a significant challenge in the field of radiation dosimetry: the accurate measurement of spatial dose distributions using Fricke gel dosimeters. Hydrogels are widely used in radiation dosimetry due to their ability to simulate the tissue-equivalent properties of human tissue, making them ideal for measuring and mapping radiation dose distributions. Among the various gel dosimeters, Fricke gels exploit the radiation-induced oxidation of ferrous ions to ferric ions and are particularly notable due to their sensitivity. The concentration of ferric ions can be measured using various techniques, including magnetic resonance imaging (MRI) or spectrophotometry. While Fricke gels offer several advantages, a significant hurdle to their widespread application is the diffusion of ferric ions within the gel matrix. This phenomenon leads to a blurring of the dose distribution over time, compromising the accuracy of dose measurements. To mitigate the issue of ferric ion diffusion, researchers have explored various strategies such as the incorporation of additives or modification of the gel composition to either reduce the mobility of ferric ions or stabilize the gel matrix. The computational method proposed leverages the power of artificial intelligence, particularly deep learning, to mitigate the effects of ferric ion diffusion that can compromise measurement precision. By employing Physics Informed Neural Networks (PINNs), the method introduces a novel way to apply physical laws directly within the learning process, optimizing the network to adhere to the principles governing ion diffusion. This is particularly advantageous for solving the partial differential equations that describe the diffusion process in 2D and 3D. By inputting the spatial distribution of ferric ions at a given time, along with boundary conditions and the diffusion coefficient, the model can backtrack to accurately reconstruct the original ion distribution. This capability is crucial for enhancing the fidelity of 3D spatial dose measurements, ensuring that the data reflect the true dose distribution without the artifacts introduced by ion migration. Here, multidimensional models able to handle 2D and 3D data were developed and tested against dose distributions numerically evolved in time from 20 to 100 h. The results in terms of various metrics show a significant agreement in both 2D and 3D dose distributions. In particular, the mean square error of the prediction spans the range 1×10-6-1×10-4, while the gamma analysis results in a 90-100% passing rate with 3%/2 mm, depending on the elapsed time, the type of distribution modeled and the dimensionality. This method could expand the applicability of Fricke gel dosimeters to a wider range of measurement tasks, from simple planar dose assessments to intricate volumetric analyses. The proposed technique holds great promise for overcoming the limitations imposed by ion diffusion in Fricke gel dosimeters.

A data-based and physics-informed Bayesian updating method for deterioration models of RC structures in marine environment

Deterioration models of reinforced concrete (RC) in marine environment, to be applied to existing structures, usually need to be calibrated with long-term in-situ data. The Bayesian model updating provides a framework to incorporate measured data into existing models to make them more realistic. The measured chloride concentrations of concrete at different depths are related to each other through the Fick’s second law, but they are treated as independent in existing updating methods, which affects the accuracy of model updating. To solve this issue, this paper proposes a data-based and physics-informed (DBPI) likelihood function to incorporate the physical law behind the measured data into Bayesian updating framework, whose validity is first confirmed through numerical examples, and then it is applied to the durability assessment of an existing wharf structure in marine environment. The parameters involved in the chloride ingress model and the critical chloride concentration model are updated using the data from durability inspections. The durability performance of the structure is then assessed using the updated models, which is consistent with the actual surface deterioration observed in the two inspections. Discussion of the updated results reveals that ignoring the physical law behind the measured data may result in incorrect inferences of the chloride ingress model and multi-mode distribution of the updated parameters, which is solved by using the proposed DBPI likelihood function, and the accuracy of Bayesian updating is significantly improved.

A Neural Network Approach to Physical Information Embedding for Optimal Power Flow

With the increasing share of renewable energy in the power system, traditional power flow calculation methods are facing challenges of complexity and efficiency. To address these issues, this paper proposes a new framework for AC optimal power flow analysis based on a physics-informed convolutional neural network (PICNN) approach, which enables the neural network to learn solutions that follow physical laws by embedding the power flow equations and other physical constraints into the loss function of the network. Compared with the traditional power flow calculation method, the calculation speed of this method is improved by 10–30 times. Compared to traditional neural network models, the method provides higher accuracy, with an average increase in accuracy of up to 2.5–10 times. In addition, this paper introduces a methodology to extract worst-case guarantees for violations of the neural network’s predicted power generation constraints, determining the worst possible violation that could result from any neural network output across the entire input domain, and taking appropriate measures to reduce the violation. The method is experimentally shown to be highly accurate and reliable for the AC optimal power flow (AC-OPF) analysis problem, while reducing the dependence on a large amount of labelled data.

Uncovering avalanche sources via acceleration measurements

Avalanche sources describe rapid and local events that govern deformation processes in various materials. The fundamental differences between an avalanche source and its associated measured acoustic emission (AE) signal are encoded in the acoustic transfer function, which undesirably modifies the properties of the source. Consequently, information about the physical characteristics of avalanche sources is scarce and its exposure poses a great challenge. We introduce a novel experimental method based on acceleration measurements, which eliminates the effect of the transfer function and distills the avalanche source. Applying this method to deformation twinning in magnesium shows that the amplitudes and characteristic times of avalanche sources are unrelated by a clear physical law. Conversely, the amplitudes and durations of AE signals are related by a power law, which is attributed to the transfer function. Using our method, we identify and compute a new feature of avalanche sources, which is directly linked to the growth rate of the twinned volume. This feature displays a power-law distribution, implying an unpredicted behavior at dynamic criticality. Simultaneously, the characteristic times of avalanche sources possess an intrinsic upper bound, indicating a predicted limit that relates to the underlying physical process of twinning.

Understanding the natural units and their hidden role in the laws of physics

The natural units of measure lauded by Max Planck more than 100 years ago are underutilized today. Many physical constants, including the Planck constant, the gravitational constant, the speed of light, vacuum permittivity, and vacuum permeability consist of natural units in their unit dimensions. The natural units are present in all formulas containing these constants. The defining characteristic of the natural units is an alignment of unit values at the Planck scale. This alignment gives a computational basis of proportionality from which the correlated properties and dynamics of elementary particles, including wavelength, period, mass, momentum, and energy, manifest in equal or inversely proportional ratios of the Planck scale. These correlations explain many of the defining equations of quantum mechanics, classical gravity, and electromagnetism.

Enhanced Quantum Metrology with Non-Phase-Covariant Noise.

The detrimental impact of noise on sensing performance in quantum metrology has been widely recognized by researchers in the field. However, there are no explicit fundamental laws of physics stating that noise invariably weakens quantum metrology. We reveal that phase-covariant noise either degrades or remains neutral to sensing precision, whereas non-phase-covariant noise can potentially enhance parameter estimation, surpassing even the ultimate precision limit achievable in the absence of noise. This implies that a non-Hermitian quantum sensor may outperform its Hermitian counterpart in terms of sensing performance. To illustrate and validate our theory, we present several paradigmatic examples of magnetic field metrology.

A Sixteen‐user Time‐bin Entangled Quantum Communication Network With Fully Connected Topology

AbstractQuantum key distribution (QKD) promises unconditionally information‐theoretic secure communication guaranteed by the laws of physics and has become one of the most crucial candidates in future security aspects. Developing a large‐scale network with a scalable and integrated scheme is of great significance for expanding the advantages of QKD protocols among multiple users. Here, a sixteen‐user fully connected quantum network by using a novel time‐bin entangled source implemented in the integrated multi‐channel periodically poled lithium niobate waveguides is proposed. Based on this entangled source, the quantum processor prepares 120 entangled photon pairs to allocate 15 links to each user by utilizing dense wavelength division multiplexing technology. To enable the users’ communication with each other simultaneously, a phase‐compensated Mach‐Zehnder Interferometer based on a Fourier‐transform setup to control the relative phase of the interferometer for all the involved wavelength channels is developed. The experimental results show that the network can support sixteen users for long‐distance communication with each other simultaneously. The novel scheme of time‐bin entangled sources paves an efficient way for implementing large‐scale quantum resources in a compact integrated platform, and the time‐bin entangled network promises a new potential for constructing large‐scale and extensible quantum networks with an integrated photonic architecture.

A physics-informed neural network approach to parameter estimation of lithium-ion battery electrochemical model

The electrochemical models (EMs) have gained increasing attention for their ability to reflect the internal states of the lithium-ion battery, yet the parameter identification is still an essential and tricky task. This paper proposes a novel physical-informed neural network (PINN) framework for the parameter identification of the EM, where three neural networks are operated in parallel to search the suitable microscopic parameters. Compared with existing neural network-based methods, PINN can utilize the prior knowledge of battery such as the physical laws that govern the system. To reduce the dimension of searching space, a parameter categorization approach is designed where parameters can be identified based on their properties under different discharge conditions. Afterwards, the PINN is integrated with EM to achieve the model prediction and parameter identification. The validation results demonstrate the good performance of the proposed method in both parameter identification and model prediction under various scenarios.

Novel physics-informed optimization framework for complex multi-physics problems: Implementation for a sweeping gas membrane distillation module

The application of advanced machine learning algorithms such as deep learning is limited for the surrogate-based process optimization of complex multi-physics problems because high-quality experimental and numerical training samples required for deep-learning model training are expensive and scarce. To address this issue, in this study, a novel physics-informed process optimization (PIPO) framework was introduced. In the first step, surrogate models based on conventional neural networks (NN) were trained using a few available high-quality training samples. In the second step, the trained NN models were coupled to the process optimization solver in which the loss of physical laws was added to the optimizer’s objective function to find optimal design points that satisfy the laws of physics. As a result, the generalization performance of the framework was greatly improved for design targets outside the training range of NN models. PIPO is substantially different from the physics-informed neural networks where the loss of physics is added to the loss function used during NN model training. The PIPO framework was used to optimize a sweeping gas membrane distillation (SGMD) module. Eight input design variables, including process and geometrical parameters, were optimized for different challenging targets to achieve the best SGMD performance in terms of ammonia recovery ratio and concentration. It was shown that for noticeably few training samples of 68 experiments, the proposed framework was able to achieve the optimization targets within a reasonable computational cost. The optimum designs were verified and analyzed in detail by high-resolution computational fluid dynamics models.

Predicting Energy Consumption for Hybrid Energy Systems toward Sustainable Manufacturing: A Physics-Informed Approach Using Pi-MMoE

Hybrid energy supply systems are widely utilized in modern manufacturing processes, where accurately predicting energy consumption is essential not only for managing productivity but also for driving sustainable development. Effective energy management is a cornerstone of sustainable manufacturing, reducing waste and enhancing efficiency. However, conventional studies often focus solely on predicting single types of energy consumption and overlook the integration of physical laws and information, which are essential for a comprehensive understanding of energy dynamics. In this context, this paper introduces a multi-task physics-informed multi-gate mixture-of-experts (pi-MMoE) model that not only considers multiple forms of energy consumption but also incorporates physical principles through the integration of physical information and multi-task modeling. Specifically, a detailed analysis of manufacturing processes and energy patterns is first conducted to study various energy types and extract relevant physical laws. Next, using industry insights and thermodynamic principles, key equations for energy balance and conversion are derived to create a physics-based loss function for model training. Finally, the pi-MMoE model framework is constructed, featuring multi-expert networks and gating mechanisms to balance cross-task knowledge sharing and expert learning. In a case study of a textile factory, the pi-MMoE model reduced electricity and steam prediction errors by 14.28% and 27.27%, respectively, outperforming traditional deep learning methods. This demonstrates that the model can improve prediction performance, providing a novel approach to intelligent energy management and promoting sustainable development in manufacturing.

Influence of powerlifting on indicators of cardiovascular functional state and the respiratory system of the organization of the collectors

The article discusses the impact of powerlifting classes on indicators of the functional state of the cardiovascular and respiratory systems of the athletes' body. It has been established that powerlifting classes contribute not only to strengthening the health and increasing the level of physical fitness of the participants, but also form a positive motivation in them for systematic physical exercises. The purpose of the article is to study powerlifting classes on the indicators of the functional state of the cardiovascular and respiratory systems of the athletes. Scientific methods were used in the research: analysis of literary sources, pedagogical observation, conversation, assessment of the functional state of the cardiovascular and respiratory systems of the applicants' body. The research concept is based on the theoretical and scientific-methodical levels of the main provisions of pedagogy, theory and methodology of physical education, laws and principles of the educational process in physical culture. The research was conducted at Zhytomyr Ivan Franko State University in 2021–2023, in which students of the second year (34 people) of the physics and mathematics and history faculties took part. During the experiment, the students of the control group studied according to the traditional program of physical education for institutions of higher education, and the students of the experimental group attended powerlifting classes. It has been proven that powerlifting has a positive effect on indicators of the functional state of the cardiovascular and respiratory systems of the athletes.

Two-Step Quadratic Programming for Physically Meaningful Smoothing of Longitudinal Vehicle Trajectories

Longitudinal vehicle trajectories suffer from errors and noise because of detection and extraction techniques, challenging their applications. Existing smoothing methods either lack physical meaning or cannot ensure solution existence and uniqueness. To address this, we propose a two-step quadratic programming method that aligns smoothed speeds and higher-order derivatives with physical laws, drivers’ behaviors, and vehicle characteristics. Unlike the well-known smoothing splines method, which minimizes a weighted sum of discrepancy and roughness in a single quadratic programming problem, our method incorporates prior knowledge of position errors into two sequential quadratic programming problems. Step 1 solves half-smoothed positions by minimizing the discrepancy between them and raw positions, subject to physically meaningful bounds on speeds and higher-order derivatives of half-smoothed positions. Step 2 solves smoothed positions by minimizing the roughness while maintaining physically meaningful bounds and allowing the deviations from raw data of smoothed positions by at most those of the half-smoothed positions and prior position errors. The second step’s coefficient matrix is not positive definite, necessitating the matching of the first few smoothed positions with corresponding half-smoothed ones, with equality constraints equaling the highest order of derivatives. We establish the solution existence and uniqueness for both problems, ensuring their well-defined nature. Numerical experiments using Next Generation Simulation (NGSIM) data demonstrate that a third-order derivative constraint yields an efficient method and produces smoothed trajectories comparable with manually re-extracted ones, consistent with the minimum jerk principle for human movements. Comparisons with an existing approach and application to the Highway Drone data set further validate our method’s efficacy. Notably, our method is a postprocessing smoothing technique based on trajectory data and is not intended for systematic errors. Future work will extend this method to lateral vehicle trajectories and trajectory prediction and planning for both human-driven and automated vehicles. This approach also holds potential for broader smoothing problems with known average error in raw data. History: This paper has been accepted for the Transportation Science Special Issue on ISTTT25 Conference. Funding: The authors extend their gratitude to the Pacific Southwest Region University Transportation Center and the University of California Institute of Transportation Studies (UC ITS) Statewide Transportation Research Program (STRP) for their valuable financial support.